Question

Given: AD || BC and ∠BCD = ∠CBE

Prove: DE || CE

a) ∠ADC = ∠CBE; AD || BC Corresponding Angles Postulate
b) ∠BDC = ∠BCE; AD || BC Corresponding Angles Postulate
c) ∠DAB = ∠CBE; AD || BC Corresponding Angles Postulate
d) ∠EDC = ∠CEB; AD || BC Corresponding Angles Postulate
e) ∠ADE = ∠CEB; AD || BC Corresponding Angles Postulate
f) ∠CDA = ∠CBE; AD || BC Corresponding Angles Postulate

Answer 1

To prove that DE || CE, we use the Corresponding Angles Postulate by noting that AD || BC and ∠BCD = ∠CBE. This implies that ∠ADC = ∠CBE, which in turn confirms the parallel lines DE || CE.

Step-by-step explanation:

To prove that DE || CE, we can use the Corresponding Angles Postulate. Since AD || BC and ∠BCD = ∠CBE, we can conclude that ∠ADC = ∠CBE as corresponding angles. Therefore, by the Corresponding Angles Postulate, DE || CE.